If $A=\left[\begin{array}{ll}1 & 2 \\ 3 & 5\end{array}\right]$ and $\alpha, \beta \in R$ are such that $\alpha A^2-\beta A=2 I$, then $\alpha^2+\beta=$

If $\left|\begin{array}{ccc}(1+\alpha)^2 & (1+2 \alpha)^2 & (1+3 \alpha)^2 \\ (2+\alpha)^2 & (2+2 \alpha)^2 & (2+3 \alpha)^2 \\ (3+\alpha)^2 & (3+2 \alpha)^2 & (3+3 \alpha)^2\end{array}\right|=k$ and $\alpha=-2$, then $k=$

7. If the system of equations $x+y+z=5, x+2 y+2 z=6$ and $x+3 y+\lambda z=\mu(\lambda, \mu \in R)$ is solvable by Matrix Inversion Method, then

If $A$ is a square matrix of order $3, \operatorname{then}\left|\operatorname{Adj}\left(\operatorname{Adj} A^2\right)\right|=$